anonymous

4 years ago

Please help on related rates i do not get it
A light is fastened on a rolling cart 1m above the floor. The light moves at 2m/s towards a 2m tall man standing 4m from a wall. How fast is the tip of the mans shadown on the wall moving when the light is 7m from the wall?

So what we have done in this picture already is that we have found the variables and the constants of the problem. The variables being x & y and the constants being the measurements given in the picture and speed that the cart is moving at. Note that the speed is given as -2. It is negative because as the cart moves closer to the man, x gets smaller. We will refer to the speed of the cart as: \[\frac{ dx }{ dt }\] (change in x with respect to t or time)

The next step now is to build a mathematical relationship between x and y. Looking at the picture we can see that there is actually a triangle inside a triangle (see
http://www.youtube.com/watch?v=1T9dHMU5pkk).
So we can then say:
\[\frac{ y-1 }{ 1 }=\frac{ 4+x }{ x }\]
We say y -1 because we don't want to the first meter and we define y to start from the ground up, not from the height of the light.